Answer:
Yes
Step-by-step explanation:
Because each value of x gives one and only one value of y
conversely, if each value of x gives more than one value for y, then it is not a function.
Answer:
18 Kg of 64 Kg represents 9/32 parts
Step-by-step explanation:
We first represent the 18lg of the 64kg as a fraction that can still be reduced:
We see that the fraction can be reduced to its half, because both the numerator and the denominator can be simplified by 2.
By so:
<h3>18 Kg of 64 Kg represents 9/32 parts</h3>
F(x) is a piecewise function defined as:
f(x) = (3/2)x when 0 <= x <= 2
or
f(x) = -(3/2)x+6 when 2 < x <= 4
g(x) is defined as:
g(x) = -(1/4)x+1 when 0 <= x <= 4
Based on the graph or through the equations we can say:
f(1) = (3/2)*1 = 1.5
g(1) = -(1/4)*1+1 = 0.75
f(3) = (3/2)*3 = 4.5
g(3) = -(1/4)*3+1 = 0.25
And the derivative values are:
f ' (1) = 3/2 = 1.5
f ' (3) = -3/2 = -1.5
g ' (1) = -1/4 = -0.25
g ' (3) = -1/4 = -0.25
which are the slopes of each line
So...
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x) ... product rule
h ' (1) = f ' (1)*g(1) + f(1)*g ' (1)
h ' (1) = 1.5*0.75 + 1.5*(-0.25)
h ' (1) = 0.75
and,
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (3) = f ' (3)*g(3) + f(3)*g ' (3)
h ' (3) = -1.5*0.25 + 4.5*(-0.25)
h ' (3) = -1.5
